Question: Solve for $x$ and $y$ using elimination. ${-6x+4y = -12}$ ${-3x-5y = -27}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-6x+4y = -12}$ $6x+10y = 54$ Add the top and bottom equations together. $14y = 42$ $\dfrac{14y}{{14}} = \dfrac{42}{{14}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-6x+4y = -12}\thinspace$ to find $x$ ${-6x + 4}{(3)}{= -12}$ $-6x+12 = -12$ $-6x+12{-12} = -12{-12}$ $-6x = -24$ $\dfrac{-6x}{{-6}} = \dfrac{-24}{{-6}}$ ${x = 4}$ You can also plug ${y = 3}$ into $\thinspace {-3x-5y = -27}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(3)}{= -27}$ ${x = 4}$